Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1507.01278

Chiral spin liquids on the kagome Lattice

Krishna Kumar·Kai Sun·Eduardo Fradkin
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of $\sxy = \frac{1}{2}$ in the regime of $XY$ anisotropy. The Dzyaloshinkii-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the $XY$ regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Krishna Kumar, Kai Sun, Eduardo Fradkin. 2015-09-09. Chiral spin liquids on the kagome Lattice. https://doi.org/10.1103/physrevb.92.094433

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exotic Spin Excitation Continuum in a Weakly Coupled Quantum Chainsaw Antiferromagnet

Collective motions in strongly interacting magnets involve many spins and are often described in terms of integer-spin excitations. However, in certain cases, the collective motion can behave as if these integer excitations break apart into smaller, particle-like entities with unusual properties. Such fractionalized excitations in quantum magnets are commonly associated either with topological order in two dimensions or with criticality in one dimension. It remains unclear how these distinct mechanisms are connected across a dimensional crossover. Here we investigate the Ti-based quantum antiferromagnet, $Cs_{8}LiNa_{3}Ti_{12}F_{48}$, in which $Ti^{3+}$ ($3d^{1}$, $S=1/2$) ions interact antiferromagnetically within distorted kagome planes. Our inelastic neutron scattering study on a single crystal reveals a frustrated network of weakly coupled spin-$1/2$ chainsaws, realizing a regime of dimensional frustration in which interchain couplings fail to establish coherent two-dimensional order. The magnetic excitation spectrum exhibits a strong continuum spanning the full measured momentum and energy phase space. In addition, the dynamic spin correlation function displays rod-like scattering in momentum space, indicating a quasi-one-dimensional nature of the magnetic correlations. These results point to fractionalized excitations with intrinsically directional character, demonstrating that signatures of one-dimensional criticality can persist within a two-dimensional lattice. Our findings establish anisotropic fractionalization as a distinct organizing principle for quantum-disordered states.

cond-mat.str-el↗
arXiv2026

Unraveling the Kagome Antiferromagnetic $3J$ Model and Its Materials: An Integrated Approach

We investigate the ground-state and finite-temperature properties of the kagome antiferromagnetic Heisenberg model with three inequivalent couplings, dubbed the $3J$ model, which is designed for the candidate Dirac quantum spin liquid (QSL) material YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_x$] (see, e.g., Zeng et al., 2024). Employing large-scale density-matrix renormalization group (DMRG) supplemented by neural quantum states (NQS) simulations, we identify an intermediate QSL phase between two magnetically ordered phases. We also find that this QSL is separated from the kagome spin liquid ground state at the isotropic limit. To establish a direct comparison with experiments, we compute the specific heat of the model by means of advanced exponential (XTRG) and tangent-space (tanTRG) thermal tensor-network methods. In the magnetically ordered phase, the specific heat over temperature exhibits a shoulder at a temperature that is a fraction of the coupling strength $J_{h}$, which disappears in the QSL phase. These universal behaviors are consistent with the experimentally observed specific heat in $3J$ materials for both ordered and QSL candidate samples. Our work thus connects microscopic models with experimentally measurable signatures, exemplifying an integrated approach to understanding QSL phenomena in frustrated quantum magnets~ (see Meng et al., 2026), with $3J$ materials serving as a representative case and providing a foundation for future studies.

cond-mat.str-el↗
arXiv2026

Quantum-interference-driven orbital density wave and high-temperature superconductivity in trilayer nickelates

Intertwined charge-density-wave (CDW) and spin-density-wave (SDW) orders are a hallmark of high-temperature superconducting multilayer nickelates. In trilayer La4Ni3O_{10}, charge correlations develop at temperatures above the onset of long-range spin order, and the characteristic ordering wavevectors satisfy $Q_{cdw} \approx 2Q_{sdw}$. Here, using a density-wave equation with vertex corrections, we show that quantum interference between short-range SDW fluctuations at $q \approx Q_{sdw}$ on the outer NiO2 layers generates an inter-outer-layer bond order at $Q_{cdw} \approx 2 Q_{sdw}$. This bond order induces a pronounced inner-layer-centered orbital order, with antiphase modulations of the Ni $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ occupations, producing strong orbital polarization but only weak total charge modulation. This intertwined bond-and-orbital order accounts for the layer-selective electronic reconstruction inferred from NMR/NQR and is consistent with Raman spectroscopy and scanning tunnelling microscopy measurements. The same orbital and spin fluctuations also cooperate to stabilize $s_{\pm}$-wave superconductivity through $M_z$ mirror-parity selection rules. Our results provide a unified microscopic framework for intertwined density-wave order and high-Tc superconductivity in multilayer nickelates.

cond-mat.str-el↗